Last updated: 2026-06-16

Antenna Length

An antenna works best when its physical size matches the wavelength of the signal it is built to handle. The starting point is the free-space wavelength, and the working element is then a simple fraction of it — a half, a quarter, or a full wavelength — trimmed slightly by the velocity factor of the conductor. This calculator takes the operating frequency $f$ and a velocity factor $k$ and returns the free-space wavelength $\lambda$ and the physical element length $L$.

Formula

where $c$ is the speed of light, $k$ is the velocity factor, and $n$ is the design fraction — one-half for a half-wave dipole, one-quarter for a quarter-wave monopole, or one for a full-wave element.

The velocity factor is a little less than 1 — about 0.95 for thin bare wire — because the wave travels slightly slower along a real conductor than through free space, so a resonant element is cut a few percent shorter than the ideal length.

Worked example

A dipole for the FM band at $100\ \text{MHz}$ with a velocity factor of 0.95.

A quarter-wave monopole at the same frequency would be about $0.712\ \text{m}$ — half the dipole length.

Half-wave dipole length vs frequency

Using a velocity factor of 0.95:

Why it matters

A resonant antenna radiates efficiently and presents a clean impedance to the transmitter, so getting the length right is the first step in any radio design. The classic shop-floor shortcut for a half-wave wire dipole is about $468 / f(\text{MHz})$ feet, which already folds in a typical velocity factor and end effects — that is why it comes out a little shorter than the pure free-space half-wavelength. The exact figure still depends on conductor diameter, insulation, and height above ground, so the calculated length is a precise starting point that is usually fine-tuned by measurement.